Time Dependent Quantum Mechanics
Quantum Physics
2012-10-29 v1
Abstract
We present a systematic method for dealing with time dependent quantum dynamics, based on the quantum brachistochrone and matrix mechanics. We derive the explicit time dependence of the Hamiltonian operator for a number of constrained finite systems from this formalism. Once this has been achieved we go on to calculate the wavevector as a function of time, in order to demonstrate the use of matrix methods with respect to several concrete examples. Interesting results are derived for elliptic curves and periodic orbits on higher dimensional non-commutative geometries.
Keywords
Cite
@article{arxiv.1210.6977,
title = {Time Dependent Quantum Mechanics},
author = {Peter G. Morrison},
journal= {arXiv preprint arXiv:1210.6977},
year = {2012}
}
Comments
34 pages, 581 equations